The part that made Feynman erupt in anger was the follow up question, "what is the total temperature of the galaxy".
It gives you the best possible estimate (in a MSE sense) for the temperature of a new star for which you know nothing about.
It may not be a great estimate (e.g, the distribution is multimodal because stars come in various types), but it doesn't seem obviously nonsensical.
The average (over 24 hours) temperature yesterday was 25˚C. You could certainly ask how that compares to other August 29ths in different years.
This even has a name ("grand mean"), so I'm surprised that someone thinks it's never useful.
> the subsamples have the same number of data points
It's unlikely to be useful in any other situation. Certainly not for averaging the temperature of a galaxy.
Both the overall mean and mean-of-means have sensible interpretations though.
Suppose you observe a random sample of stars and find their temperatures to be 6000, 6250, 6750, and 7000C. The best possible guess[0] for the temperature of a new star drawn from that population is 6500C. The average temperature of all the starstuff may be different if one star is larger than another, but that's an answer to a slightly different question.
In fact, I would argue that the mean-of-means is often a more appropriate summary statistic than the overall mean of the observations when there are repeated measurements.
[0] Under L2 loss, with no prior, etc etc
[0] https://www.hup.harvard.edu/catalog.php?content=reviews&isbn...
[1] https://www.maa.org/external_archive/devlin/LockhartsLament....
>The reason was that the books were so lousy. They were false. They were hurried. They would try to be rigorous, but they would use examples (like automobiles in the street for "sets") which were almost OK, but in which there were always some subtleties. The definitions weren't accurate. Everything was a little bit ambiguous – they weren't smart enough to understand what was meant by "rigor." They were faking it. They were teaching something they didn't understand, and which was, in fact, useless, at that time, for the child.
>[...] That's the way everything was: Everything was written by somebody who didn't know what the hell he was talking about, so it was a little bit wrong, always! And how we are going to teach well by using books written by people who don't quite understand what they're talking about, I cannot understand. I don't know why, but the books are lousy; UNIVERSALLY LOUSY!